Normalized intensity of the overall reflected probe light (a) and the normalized amplitude of the Fourier transformed, longitudinal Brillouin scattering signal (b) for different sample layer thicknesses. The sample configuration was a MBE iron transducer, DC704 at 200 K as the liquid and a linear slope detection substrate with a Brillouin scattering frequency of 41 GHz. The optical and acoustic cavity effects can be significant in some cases, as clearly visible in these plots.
Sketch of multilayer structure which forms both an acoustic and optical cavity. The cavity is a result of a liquid layer 1 of thickness squeezed in between an opaque or semi-transparent, optically reflective transducer film 0 and a transparent detection substrate 2. Longitudinal and/or shear acoustic waves, generated in the transducer film, propagate in the z-direction through the adjacent liquid layer and into the detection substrate. At time , we consider the acoustic wave, denoted by , localized at a position away from the transducer-liquid interface where it induces a small change in the permittivity tensor of the substrate. Through the photoelastic effect, this perturbation backscatters a small portion of the incoming probe electric field denoted as , and a small portion of the electric field reflected by the transducer, , denoted as or . Some portion of the incoming electric field reflected by the transducer makes one or more round-trips in the optical cavity formed by the liquid layer before it finally escapes the cavity as and . All these outgoing electric fields superpose and interfere with each other and produce a heterodyne coherent Brillouin scattering signal at the photodiode.
(a) Sketch of shear detection setup in a front-back pump-probe geometry and (b) close-up of sample assembly. (b) A large diameter optical pump pulse (or pulse sequence) incident on a specialized shear transducer thin film launched both longitudinal and vertically polarized transverse acoustic wavepackets into an adjacent liquid layer of thickness (considered of constant thickness over the probe spot area). After propagation through the liquid layer, the acoustic waves were detected in a transparent detection substrate by TDBS. Tightly focused, vertically polarized probe light interacted with the propagating, vertically polarized shear acoustic wave fronts which backscattered a small portion of the light with a 90° polarization rotation (depolarized TDBS) as the signal beam (Sig). The portion of the probe light that was reflected by the sample structure (mainly by the metallic transducer layer) served as the reference beam (Ref). In case of longitudinal acoustic waves, the vertically polarized probe light was backscattered without a change in polarization. (a) A balanced photo-detection approach was capable of recording the extremely weak depolarized shear Brillouin scattering signals with sufficient signal-to-noise levels. The polarizations of all reflected probe light components (Sig and Ref) from the sample were rotated 45° by means of a HWP and were subsequently separated into their horizontally and vertically polarized components by means of a polarizing beam splitter (PBS) cube. Each output contained approximately half the initial light intensity, with the Brillouin oscillation signal modulated with opposite signs at the two detectors. Differential detection (diode A-diode B) subtracted out common noise while adding the signal. The sample assembly was mounted on a computer-controlled motorized stage whose translation (X position) allowed access to liquid thicknesses between ∼0 nm and several microns.
Illustration of the approach to access a wide range of longitudinal and shear acoustic frequencies. (a) Standard configuration for time-domain Brillouin scattering in the detection substrate. An oblique probe incidence angle is a requirement for detection of shear waves since the scattering efficiency diminishes toward zero as the backscattering angle is approached. Adjustment of the probe incidence angle in air changes the angle in the substrate and thereby allows us to tune the Brillouin scattering frequency. However, the maximum angle in the substrate is limited by refraction and sample holder design to typically less than 30°, limiting the tuning range of the Brillouin frequencies to 10%–15% for a given substrate material. The use of a prism (b) accesses significantly larger probe angles in the detection substrate, up to 60°, which corresponds to a Brillouin frequency range of about 50%. In this design, the X direction on the sample must be perpendicular to the plane defined by the incident and emerging probe light.
(a) Sketch of curved slope sample design, referred to as “flat-curved” sample design, and usually constructed with a plano-convex lens with radius of curvature of 2.5 m. (b) Linear slope sample design, referred to as “flat-polished” sample design and built with a specially prepared flat substrate (three polished areas are labeled P, Q, and R). Their respective images (on the right) show Newton’s interference rings/fringes (images were taken with 790 nm light). Measurements on all samples were made at several lateral (X) positions corresponding to different liquid layer thicknesses.
Signals from shear waves after propagation through two different thicknesses of glycerol (two distinct positions X1 and X2 on the sample corresponding to two distinct liquid layer thicknesses and ) which were generated by a canted iron transducer thin film on a glass generation side substrate and detected in a sapphire detection substrate. (a) Time derivative of the recorded polarization-rotated signal intensity. The excitation pulse sequence is visible between 0 and 150 ps, followed by oscillations due to coherent shear wave propagation in the sapphire detection substrate. (b) Acoustic amplitude spectra of both signals, FFT1 and FFT2, and (c) their corresponding Fourier phases, and . The phase and amplitude differences yield the acoustic speed and attenuation coefficient, respectively, in the liquid at the specified Brillouin frequency.
(a) Interpolated 2D plot of about 50 longitudinal wave data sets, recorded from glycerol at room temperature in a flat-curved substrate configuration, as a function of probe pulse delay time (plotted vertically) at different lateral (X) positions across the sample (displayed horizontally). The X steps are much larger than the 20 μm diameter of the focused probe laser beam, but they are sufficiently small that the signal between steps can be interpolated reliably. A single excitation pulse rather than a pulse sequence was used. The electronic peaks at ps were used as a time and amplitude reference. The high-frequency signal oscillations at 41 GHz correspond to Brillouin scattering from longitudinal acoustic waves in the BK7 glass substrate while the low-frequency oscillations at 18 GHz correspond to Brillouin scattering from the acoustic waves in liquid glycerol. Near the center of the sample (X≈0) the lens and the substrate were almost in direct contact, and signal oscillations due to acoustic propagation in the substrate begin promptly. Away from the center the signal oscillations due to acoustic wave propagation in the substrate are further delayed and phase shifted, and these oscillations are preceded by lower-frequency oscillations due to acoustic wave propagation in the liquid. (b) Normalized amplitude values and (c) phase shifts of the 41 GHz high-frequency signal oscillations extracted from Brillouin scattering in the substrate. The liquid topography as determined by the lens curvature and calculated by Eq. (25) is also indicated.
(a) Interpolated 2D plot of about 100 longitudinal wave data sets recorded in DC704 at 200 K as a function of probe delay time (plotted vertically) at different lateral positions across the sample (displayed horizontally). The electronic peak at ps has been used as a time and amplitude reference. The liquid thickness increases almost linearly with X in this sample consisting of a polished and a flat substrate. The high-frequency signal oscillations at 41 GHz, clearly visible at small X positions and somewhat masked by low-frequency oscillations at 21 GHz from Brillouin scattering in glassy DC704, correspond to Brillouin scattering from longitudinal acoustic waves in the BK7 glass detection substrate. The phase of the Brillouin scattering in the glass detection substrate changes with liquid thickness and therefore is a function of X position. (b) The decay of the acoustic amplitude with respect to the liquid thickness gives the acoustic attenuation coefficient. Note that oscillations in the acoustic amplitude at small liquid thicknesses (corresponding to small X positions) like those in Fig. 1(b) cannot be observed in this plot due to large steps in liquid thickness. (c) Fourier analysis yields the 41 GHz oscillation phases from which the DC704 phase velocity and layer thickness variation with X can be determined.
Frequency dependences of shear and longitudinal acoustic velocities (a) and attenuation coefficients (b) in liquid glycerol at room temperature obtained by measurements with multiple Brillouin scattering angles using glass and sapphire detection substrates. The 20–30 GHz shear and 30–40 GHz longitudinal data were obtained at multiple angles of incidence with a glass detection substrate, while the 30–60 GHz shear and 50–100 GHz longitudinal data were obtained at multiple angles of incidence with a sapphire detection substrate. Adapted from Ref. 31.
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